Projections down to a space spanned by the significant variables

Projections down to a space spanned by the significant variables 

After a fractional factorial design has been run with a view to screen the experimental variables some variable may turn out to be insignificant. In such cases, the experiments which have been run can be used to obtain more detailed information on the remaining variables if the insignificant variable is left out. It is possible to consider the experiments already performed as a larger fraction of design in the remaining variables. 

We can make a projection of the original design down to the space spanned by the remaining variables. The principles are Illustrated in Fig. 6.12, in which a 2 fractional factorial design is projected down to the planes spanned by the remaining variables. 

The consequences for the confounding patterns, if some variable turns out to be not significant, can be determined from the confounding pattern of the fractional design as all effects associated with the insignificant variables can be removed from the aliases obtained from each column. This technique is not entirely fool-proof and should not be routinely applied. It is sometimes a useful technique for obtaining new ideas. These ideas must then, of course, be checked through experiments. 

Example Two insignificant variables in a 2 flractional factorial design 

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